In the last two decades, the terms waste management and climate conservation have become major worldwide issues with global warming and its opposing sides on the future of the planet. The main purpose of this study is the modeling of Anaerobic Digestion (AD) that can be utilized to analyze various operational strategies in order to recover biogas from Maize Waste (MW). The production of methane is the go of this paper, which requires the inclusion of biological and Physico-chemical models in order to describe the whole process of methanization. One of the best choice in the modeling of such biological issues is the phenomenological model of Anaerobic Digestion (AD), which is the most complete model for wastewater treatment. This model is called ADM1, and it is an integrated model that describes very well the transformation of the Organic Matter (OM) into soluble components, then into biogas as the final phase of this biological conversion. The modeling tools for anaerobic degradation make the subject of this study. The completion of the ADM1 model is done by the resolution of systems of Differential Equations (DE) by a numerical method. In this study, the Runge-Kutta method is used to resolve the ADM1 model.